Replacing Radiator, should I replace it THEN do an engine radiator flush

I know you mentioned no access to a hose.
But i think its necessary to get rid of the rad flush out of the engine.

Had a jeep a while back, pulled thermostat,replaced housing and disconnected hoses off rad, engine cold and stuffed garden hose into lower rad hose and a rag to close gap.
Run hose start engine and let the fresh water carry out all the junk.